A machine of a type to which the present invention relates is described in German Published Patent Application No. DE-AS 1 611 239. This machine can operate both in raised letters, or offset printing mode. The cylinders of the printing machine can operate in either direction, so that the paper path on which printing is to be effected can be suitably selected. The paper path is passed through the printing system which includes two plate cylinders and two blanket cylinders. In offset printing, the plate on the plate cylinder continuously has damping liquid applied thereto prior to inking thereof. For damping, a slinger-type damping system is provided, selectively positionable between two positions on the plate cylinger. When raised letter printing is to be effected, the slinger damping system is removed.